1. 10.2 Mole-Mass and Mole- Volume Relationships 1 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. Chapter 10 Chemical Quantities 10.1 The Mole: A Measurement of Matter 10.2 Mole-Mass and Mole- Volume Relationships 10.3 Percent Composition and Chemical Formulas

2. 10.2 Mole-Mass and Mole- Volume Relationships 2 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. How can you calculate the pieces of a substance in a given mass or volume? CHEMISTRY & YOU Guess how many pennies are in the container. In a similar way, chemists use the relationships between the mole and quantities such as mass, volume, and number of particles to solve problems in chemistry.

3. 10.2 Mole-Mass and Mole- Volume Relationships 3 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. The Mole-Mass Relationship How do you convert the mass of a substance to the number of moles of the substance? The Mole-Mass Relationship

4. 10.2 Mole-Mass and Mole- Volume Relationships 4 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. Use the molar mass of an element or compound to convert between the mass of a substance and the moles of the substance. The Mole-Mass Relationship

5. 10.2 Mole-Mass and Mole- Volume Relationships 5 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. Use the molar mass of an element or compound to convert between the mass of a substance and the moles of the substance. molar mass 1 mol molar mass or The Mole-Mass Relationship The conversion factors for these calculations are based these relationships.

6. 10.2 Mole-Mass and Mole- Volume Relationships 6 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. In some situations the term molar mass may be unclear. Suppose you were asked for the molar mass of oxygen. The Mole-Mass Relationship

7. 10.2 Mole-Mass and Mole- Volume Relationships 7 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. In some situations the term molar mass may be unclear. Suppose you were asked for the molar mass of oxygen. The Mole-Mass Relationship –If you assume molecular oxygen (O 2 ), then the molar mass is 32.0 g/mol (2 × 16.0 g/mol). –If you assume elemental oxygen (O), then the answer is 16.0 g/mol.

8. 10.2 Mole-Mass and Mole- Volume Relationships 8 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. In some situations the term molar mass may be unclear. Suppose you were asked for the molar mass of oxygen. You can avoid confusion such as this by using the formula of the substance, in this case O 2 or O. The Mole-Mass Relationship –If you assume molecular oxygen (O 2 ), then the molar mass is 32.0 g/mol (2 × 16.0 g/mol). –If you assume elemental oxygen (O), then the answer is 16.0 g/mol.

9. 10.2 Mole-Mass and Mole- Volume Relationships 9 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. Items made out of aluminum, such as aircraft parts and cookware, are resistant to corrosion because the aluminum reacts with oxygen in the air to form a coating of aluminum oxide (Aℓ 2 O 3 ). This tough, resistant coating prevents any further corrosion. What is the mass, in grams, of 9.45 mol of aluminum oxide? Sample Problem Converting Moles to Mass

10. 10.2 Mole-Mass and Mole- Volume Relationships 10 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. The mass of the compound is calculated from the known number of moles of the compound. The desired conversion is moles → mass. KNOWN number of moles = 9.45 mol Aℓ 2 O 3 UNKNOWN mass = ? g Aℓ 2 O 3 Sample Problem Analyze List the known and the unknown. 1

11. 10.2 Mole-Mass and Mole- Volume Relationships 11 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. First determine the mass of 1 mol of Aℓ 2 O 3. Sample Problem Calculate Solve for the unknown. 2 2 mol Aℓ × = 54.0 g Aℓ 3 mol O × = 48.0 g O 27.0 g Aℓ 1 mol Aℓ 16.0 g O 1 mol O 1 mol Aℓ 2 O 3 = 54.0 g Aℓ + 48.0 g O= 102.0 g of Aℓ 2 O 3

12. 10.2 Mole-Mass and Mole- Volume Relationships 12 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. Identify the conversion factor needed. 1 mol Aℓ 2 O 3 102.0 g Aℓ 2 O 3 Sample Problem Calculate Solve for the unknown. 2 1 mol Aℓ 2 O 3 102.0 g Aℓ 2 O 3 or

13. 10.2 Mole-Mass and Mole- Volume Relationships 13 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. Multiply the given number of moles by the conversion factor. Sample Problem Calculate Solve for the unknown. 2 9.45 mol Aℓ 2 O 3 × 102.0 g Aℓ 2 O 3 1 mol Aℓ 2 O 3 = 963.9 g Aℓ 2 O 3 = 964 g Aℓ 2 O 3

14. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. The number of moles of Aℓ 2 O 3 is approximately 10, and each has a mass of approximately 100 g. The answer should be close to 1000 g. The answer has been rounded to the correct number of significant figures. Sample Problem Evaluate Does the result make sense? 3

15. 10.2 Mole-Mass and Mole- Volume Relationships 15 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. When iron is exposed to air, it corrodes to form a red- brown rust. Rust is iron(III) oxide (Fe 2 O 3 ). How many moles of iron(III) oxide are contained in 92.2 g of pure Fe 2 O 3 ? Converting Mass to Moles Sample Problem

16. 10.2 Mole-Mass and Mole- Volume Relationships 16 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. The number of moles of the compound is calculated from the known mass of the compound. The conversion is mass → moles. KNOWN mass = 92.2 g Fe 2 O 3 UNKNOWN number of moles = ? mol Fe 2 O 3 Sample Problem Analyze List the known and the unknown. 1

17. 10.2 Mole-Mass and Mole- Volume Relationships 17 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. First determine the mass of 1 mol of Fe 2 O 3. 1 mol Fe 2 O 3 = 112 g Fe + 48.0 g O 2 mol Fe ×= 112 g Fe 56 g Fe 1 mol Fe 3 mol O ×= 48.0 g O 16.0 g O 1 mol O Sample Problem Calculate Solve for the unknown. 2 = 160 g Fe 2 O 3

18. 10.2 Mole-Mass and Mole- Volume Relationships 18 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. Identify the conversion factor relating grams of Fe 2 O 3 to moles of Fe 2 O 3. 160 g Fe 2 O 3 1 mol Fe 2 O 3 Note that the known unit (g) is in the denominator and the unknown unit (mol) is in the numerator. Sample Problem Calculate Solve for the unknown. 2

19. 10.2 Mole-Mass and Mole- Volume Relationships 19 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. Multiply the given mass by the conversion factor. 92.2 g Fe 2 O 3 × 1 mol Fe 2 O 3 160 g Fe 2 O 3 = 0.57625 mol Fe 2 O 3 Sample Problem Calculate Solve for the unknown. 2 = 0.576 mol Fe 2 O 3

20. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. The given mass (about 90 g) is slightly larger than the mass of one-half mole of Fe 2 O 3 (about 80 g), so the answer should be slightly larger than one-half (0.5) mol. Sample Problem Evaluate Does the result make sense? 3

21. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. You know how many grams of a substance you have and want to find out how many moles this is. What other information do you need to know, and where can you find it?

22. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. You know how many grams of a substance you have and want to find out how many moles this is. What other information do you need to know, and where can you find it? You also need to know the molar mass, which you can calculate using the molecular formula and the molar masses of the constituent elements listed in the periodic table of elements.

23. 10.2 Mole-Mass and Mole- Volume Relationships 23 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. The Mole-Volume Relationship How do you convert the volume of a gas at STP to the number of moles of the gas? The Mole-Volume Relationship STP stands for STANDARD TEMPERATURE and PRESSURE

24. 10.2 Mole-Mass and Mole- Volume Relationships 24 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. The Mole-Volume Relationship Unlike liquids and solids, the volumes of moles of gases, measured under the same physical conditions, are much more predictable. The Mole-Volume Relationship

25. 10.2 Mole-Mass and Mole- Volume Relationships 25 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. Notice that the volumes of one mole of different solid and liquid substances are not the same. The Mole-Volume Relationship The volumes of one mole of glucose (blood sugar) and one mole of parachlorobenzene (moth crystals) are much larger than the volume of one mole of liquid water.

26. 10.2 Mole-Mass and Mole- Volume Relationships 26 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. Avogadro’s hypothesis states that equal volumes of gases at the same temperature and pressure contain equal numbers of particles. The Mole-Volume Relationship Avogadro’s Hypothesis

27. 10.2 Mole-Mass and Mole- Volume Relationships 27 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. The particles that make up different gases are not the same size. The Mole-Volume Relationship * Whether the particles are large or small, large amounts of space exist between individual particles of gas. Avogadro’s Hypothesis

28. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. Avogadro’s Hypothesis The Mole-Volume Relationship Same amount of space and same amount of particles.

29. 10.2 Mole-Mass and Mole- Volume Relationships 29 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. The volume of a gas varies with a change in temperature or a change in pressure. The Mole-Volume Relationship Avogadro’s Hypothesis

30. 10.2 Mole-Mass and Mole- Volume Relationships 30 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. The volume of a gas varies with a change in temperature or a change in pressure. The Mole-Volume Relationship Avogadro’s Hypothesis Due to variations in temperature and pressure, the volume of a gas is usually measured at STP.

31. 10.2 Mole-Mass and Mole- Volume Relationships 31 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. The volume of a gas varies with a change in temperature or a change in pressure. The Mole-Volume Relationship Avogadro’s Hypothesis Due to variations in temperature and pressure, the volume of a gas is usually measured at STP. Standard temperature and pressure (STP) means a temperature of 0°C and a pressure of 101.3 kPa, or 1 atmosphere (atm).

32. 10.2 Mole-Mass and Mole- Volume Relationships 32 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. At STP, 1 mol, or 6.02 × 10 23 representative particles, of any gas occupies a volume of 22.4 L. The quantity, 22.4 L, is called the molar volume of a gas. The Mole-Volume Relationship Avogadro’s Hypothesis

33. 10.2 Mole-Mass and Mole- Volume Relationships 33 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. The molar volume is used to convert between the number of moles of gas and the volume of the gas at STP. Calculating the Volume and Moles of a Gas at STP 22.4 L 1 mol 22.4 L and The Mole-Volume Relationship The conversion factors for these calculations are based on the relationship 22.4 L = 1 mol at STP.

34. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. You can use these conversion factors to convert a known number of moles of gas to the volume of the gas at STP. Similarly, you can convert a known volume of gas at STP to the number of moles of the gas. The Mole-Volume Relationship Calculating the Volume and Moles of a Gas at STP 22.4 L 1 mol 22.4 L and

35. 10.2 Mole-Mass and Mole- Volume Relationships 35 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. Sulfur dioxide (SO 2 ) is a gas produced by burning coal. It is an air pollutant and one of the causes of acid rain. Determine the volume, in liters, of 0.60 mol SO 2 gas at STP. Sample Problem Calculating Gas Quantities at STP

36. 10.2 Mole-Mass and Mole- Volume Relationships 36 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. Since SO 2 is a gas, the volume at STP can be calculated from the known number of moles. KNOWNS number of moles = 0.60 mol SO 2 1 mol SO 2 = 22.4 L SO 2 at STP UNKNOWN volume = ? L SO 2 Sample Problem Analyze List the knowns and the unknown. 1

37. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. First identify the conversion factor relating moles of SO 2 to volume of SO 2 at STP. 22.4 L SO 2 1 mol SO 2 Sample Problem Calculate Solve for the unknown. 2

38. 10.2 Mole-Mass and Mole- Volume Relationships 38 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. Multiply the given number of moles by the conversion factor. Sample Problem Calculate Solve for the unknown. 2 0.60 mol SO 2 × 22.4 L SO 2 1 mol SO 2 = 13.44 L SO 2 = 13 L SO 2

39. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. One mole of any gas at STP has a volume of 22.4 L, so 0.60 mol should have a volume slightly larger than one- half of a mole or 11.2 L. The answer should have two significant figures. Sample Problem Evaluate Does the result make sense? 3

40. 10.2 Mole-Mass and Mole- Volume Relationships 40 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. A gas-filled balloon will either sink or float in the air depending on whether the density of the gas inside the balloon is greater or less than the density of the surrounding air. Calculating Molar Mass and Density The Mole-Volume Relationship Different gases have different densities. Usually the density of a gas is measured in grams per liter (g/L) and at a specific temperature.

41. 10.2 Mole-Mass and Mole- Volume Relationships 41 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. The density of a gas at STP and the molar volume at STP (22.4 L/mol) can be used to calculate the molar mass of the gas. The Mole-Volume Relationship Calculating Molar Mass and Density

42. 10.2 Mole-Mass and Mole- Volume Relationships 42 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. The density of a gas at STP and the molar volume at STP (22.4 L/mol) can be used to calculate the molar mass of the gas. Similarly, the molar mass of a gas and the molar volume at STP can be used to calculate the density of a gas at STP. The Mole-Volume Relationship Calculating Molar Mass and Density

43. 10.2 Mole-Mass and Mole- Volume Relationships 43 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. The density of a gaseous compound containing carbon and oxygen is found to be 1.964 g/L at STP. What is the molar mass of the compound? Sample Problem Calculating the Molar Mass of a Gas at STP

44. 10.2 Mole-Mass and Mole- Volume Relationships 44 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. The molar mass of the compound is calculated from the known density of the compound and the molar volume at STP. KNOWNS density = 1.964 g/L 1 mol of gas at STP = 22.4 L UNKNOWN molar mass = ? g/mol Sample Problem Analyze List the knowns and the unknown. 1

45. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. Sample Problem First identify the conversion factor needed to convert density to molar mass. 22.4 L 1 mol Calculate Solve for the unknown. 2

46. 10.2 Mole-Mass and Mole- Volume Relationships 46 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. Multiply the given density by the conversion factor. Sample Problem Calculate Solve for the unknown. 2 1.964 g 1 L 22.4 L 1 mol × = 43.9936 g/mol = 43.99 g/mol

47. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. The ratio of the calculated mass (44.0 g) to the volume (22.4 L) is about 2, which is close to the known density. The answer should have three significant figures. Sample Problem Evaluate Does the result make sense? 3

48. 10.2 Mole-Mass and Mole- Volume Relationships 48 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. The mole is at the center of your chemical calculations. The Mole-Volume Relationship To convert from one unit to another, you must use the mole as an intermediate step.

49. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. Why does one mole of any gas occupy the same volume (22.4 L) at standard temperature and pressure?

50. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. Why does one mole of any gas occupy the same volume (22.4 L) at standard temperature and pressure? Gas molecules do vary in size, just like molecules of solids and liquids, but the particles in a gas are always so far apart that the change in volume of the molecules doesn’t change the volume the gas occupies at STP.

51. 10.2 Mole-Mass and Mole- Volume Relationships 51 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. Use the molar mass of an element or compound to convert between the mass of a substance and the moles of the substance. The molar volume is used to convert between the number of moles of gas and the volume of the gas at STP. Key Concepts

52. 10.2 Mole-Mass and Mole- Volume Relationships 52 > Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.. END OF 10.2